Find the Derivative - d/dx y=4x^2-5x

Problem

d()/d(x)*(4*x2−5*x)

Solution

1. Apply the sum/difference rule of differentiation, which states that the derivative of a sum or difference is the sum or difference of the derivatives.

d()/d(x)*(4*x2−5*x)=(d(4)*x2)/d(x)−(d(5)*x)/d(x)

2. Apply the constant multiple rule to move the constants outside of the derivatives.

(d(4)*x2)/d(x)−(d(5)*x)/d(x)=4d(x2)/d(x)−5d(x)/d(x)

3. Apply the power rule, which states that d(xn)/d(x)=n*x(n−1)

4*(2*x(2−1))−5*(1*x(1−1))

4. Simplify the exponents and coefficients to find the final derivative.

8*x−5

Final Answer

d()/d(x)*(4*x2−5*x)=8*x−5

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